A nonlocal game \(G\)  is specified by a quadruple \((\mathcal {X},\mathcal {A},\mu ,D)\)  which corresponds to the following scenario: a referee first samples a pair of questions \((x,y)\)  from a distribution \(\mu \)  over a finite product set \(\mathcal {X} \times \mathcal {X}\)  and sends \(x\)  to prover A and \(y\)  to prover B. The provers respond with answers \(a,b \in \mathcal {A}\)  respectively and the referee accepts if and only if \(D(x,y,a,b) = 1\) , where \(D: \mathcal {X} \times \mathcal {X} \times \mathcal {A} \times \mathcal {A} \rightarrow \lbrace 0,1\rbrace \)  is a decision predicate. Different kinds of restrictions on the provers' allowed actions to determine their answers lead to different optimal success probabilities for them in the game.
The tensor code test described earlier is an example of a nonlocal game, and the analysis of it with deterministic non-communicating provers is a key component in the aforementioned complexity-theoretic results, e.g. [1]}.
